This chapter explains analytic or inferential statistics, which extend beyond description to draw conclusions about populations based on sample data. Core concepts such as probability, sampling, hypothesis testing, and confidence intervals are introduced, providing the framework for statistical inference. Common statistical tests, including t-tests, chi-square tests, and regression models, are explained with guidance on their assumptions and appropriate use. The distinction between statistical and clinical significance is emphasised, encouraging cautious interpretation of p-values and consideration of effect sizes. The chapter also addresses issues such as multiple testing, type I and type II errors, and the role of power and sample size in study design. Practical examples illustrate the application of inferential statistics in evaluating treatment effects, identifying risk factors, and testing public health hypotheses. Strengths of inferential methods include their ability to generalise findings, while limitations include vulnerability to misuse and misinterpretation if assumptions are violated. The chapter concludes by underscoring the importance of combining statistical expertise with substantive knowledge. This chapter maps to syllabus sections 2.3–2.6, which cover hypothesis testing, probability, regression, confidence intervals, and the interpretation of p-values.

In setting up your model, include those variables, in addition to the risk factor or group assignment, that have been theorized or shown in prior research to be confounders or those that empirically are associated with the risk factor and the outcome in bivariate analysis.

Exclude variables that are on the intervening pathway between the risk factor and outcome, those that are extraneous because they are not on the causal pathway, redundant variables, and variables with a lot of missing data.

Sample size calculation for multivariable analysis is complicated but statistical programs exist to help you to calculate it. Missing data on independent variables can compromise your multivariable analysis. Several methods exist to compensate for missing independent data including deleting cases, using indicator variables to represent missing data and estimating the value of missing cases. Methods also exist for estimating missing outcome data using other data you have about the subject and multiple imputation.